The Theory of Economic Complexity

Economic complexity methods aim to estimate the combined presence of economic factors without having to explicitly define them. A key method in this literature is the Economic Complexity Index or ECI, an eigenvector derived from specialization matrices that explains variation in economic growth, inequality, and sustainability. Yet, despite the widespread use of ECI in economic development, economic geography, and innovation studies, we still lack a principled theory that can deduce it from a mechanistic model. Here, we calculate $ECI$ analytically for a model where the output of an economy in an activity increases if the economy is more likely to be endowed with the factors required by the activity. We derive ECI analytically and numerically and show that it is a monotonic function of the probability that an economy is endowed with many factors, validating the idea that ECI is an agnostic estimate of the presence of multiple factors in an economy. We then generalize this result to other production functions and to a short-run equilibrium framework with prices, wages, and consumption, finding that the derived wage function is consistent with economies converging to an income that is compatible with their complexity. Finally, we show this model explains differences in the shapes of networks of related activities, such as the product space and the research space. These findings solve long standing puzzles in the literature and validate metrics of economic complexity as estimates of the combined presence of multiple factors.